They are generally thought to be called wisdom teeth because they appear so late—much later than the other teeth, at an age where people are supposedly wiser than as a child, when the other teeth erupt.
Potential problems caused by the presence of properly grown-in wisdom teeth include infections caused by food particles easily trapped in the jaw area behind the wisdom teeth where regular brushing and flossing is difficult and not effective. Such infections may be frequent, and cause considerable pain and medical danger.
A wisdom tooth is extracted to correct an actual problem or to prevent problems that may come up in the future. Wisdom teeth are extracted for two general reasons: either the wisdom teeth have already become impacted, or the wisdom teeth could potentially become problematic if not extracted.
Another reason to have a wisdom tooth removed if the tooth has grown in improperly, causing the tongue to brush up against it. The tongue can tolerate it for a limited time, until it causes a painful sensation, to the point where the sheer pain can numb the tongue affected, and the area around it (part of the lips, and the cheek).